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Limits of Stability Conditions and T...

Robotis, Antonios-Alexandros,

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Limits of Stability Conditions and Their Geometry /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Limits of Stability Conditions and Their Geometry // Antonios-Alexandros Robotis.
Author:	Robotis, Antonios-Alexandros,
Description:	1 electronic resource (172 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
Contained By:	Dissertations Abstracts International86-12B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31999273
ISBN:	9798283137810

Limits of Stability Conditions and Their Geometry /
Robotis, Antonios-Alexandros,

Limits of Stability Conditions and Their Geometry /Antonios-Alexandros Robotis. - 1 electronic resource (172 pages)

Source: Dissertations Abstracts International, Volume: 86-12, Section: B.

After giving a brief survey of the study of derived categories in algebraic geometry, I present a pair of research papers. The first, joint with Daniel Halpern-Leistner and Jeffrey Jiang, introduces the notion of quasi-convergent paths in the space of stability conditions. We prove that quasi-convergent paths give rise to decompositions of triangulated categories (e.g. derived categories of coherent sheaves on a variety) and that conversely for a smooth and proper dg-category all polarized semiorthogonal decompositions arise in this fashion.In the second paper, I study the geometry of certain moduli spaces of genus 0 curves with differentials called multiscale lines which are introduced in [HLR]. I prove that these spaces are complex projective varieties by giving an explicit isomorphism with a blow-up of a linear subspace arrangement of projective space. I use this isomorphism to connect these spaces of multiscale lines with other spaces in the literature studied by Zahariuc.

English

ISBN: 9798283137810Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Algebraic geometry

Limits of Stability Conditions and Their Geometry /
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245 1 0 $a Limits of Stability Conditions and Their Geometry / $c Antonios-Alexandros Robotis.
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300 $a 1 electronic resource (172 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
500 $a Advisors: Halpern-Leistner, Daniel Committee members: Knutson, Allen; Riley, Tara.
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520 $a After giving a brief survey of the study of derived categories in algebraic geometry, I present a pair of research papers. The first, joint with Daniel Halpern-Leistner and Jeffrey Jiang, introduces the notion of quasi-convergent paths in the space of stability conditions. We prove that quasi-convergent paths give rise to decompositions of triangulated categories (e.g. derived categories of coherent sheaves on a variety) and that conversely for a smooth and proper dg-category all polarized semiorthogonal decompositions arise in this fashion.In the second paper, I study the geometry of certain moduli spaces of genus 0 curves with differentials called multiscale lines which are introduced in [HLR]. I prove that these spaces are complex projective varieties by giving an explicit isomorphism with a blow-up of a linear subspace arrangement of projective space. I use this isomorphism to connect these spaces of multiscale lines with other spaces in the literature studied by Zahariuc.
546 $a English
590 $a School code: 0058
650 4 $a Mathematics. $3 515831
650 4 $a Applied mathematics. $3 2122814
650 4 $a Computational physics. $3 3343998
653 $a Algebraic geometry
653 $a Derived categories
653 $a Moduli of curves
653 $a Quasi-convergent paths
653 $a Zahariuc
690 $a 0405
690 $a 0216
690 $a 0364
710 2 $a Cornell University. $b Mathematics. $e degree granting institution. $3 3816358
720 1 $a Halpern-Leistner, Daniel $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-12B.
790 $a 0058
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31999273